Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

56 406 is the product of two consecutive numbers. What are these two numbers?

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

What is the least square number which commences with six two's?

Play this game and see if you can figure out the computer's chosen number.

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Find the highest power of 11 that will divide into 1000! exactly.

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Can you find what the last two digits of the number $4^{1999}$ are?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Given the products of adjacent cells, can you complete this Sudoku?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

What is the smallest number of answers you need to reveal in order to work out the missing headers?

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

This task combines spatial awareness with addition and multiplication.

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Here is a chance to play a version of the classic Countdown Game.

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.